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Just a note

This is the standard normal distribution, whose intimate details are to be found in any book of statistical tables. Because it's 'tails' are infinitely long, we cannot show all of this monster - but it is obviously smooth and symmetrical.

This figure shows two ways of graphing this distribution - as a bell-shaped 'density function', or as an s-shaped 'cumulative function'. Notice that the highest point on the bell shaped curve is equivalent to the 'point of inflection' of the s-shaped curve - in other words, where the cumulative function stops curving upwards, and starts to curve in the opposite direction. This point is the mean, median and mode.

The bell-shaped curve has two points of inflection, both of which lie one standard deviation from the mean - although we have only labelled one of these points.